The generator matrix

 1  0  0  1  1  1  1  1  1  1  1  1  1 a^2*X  1  1 a^2*X  1  0  X  1  1  1  X a*X  1  1  1  1  1  1  1  1  1  0  1  1  X  1
 0  1  0  0  0 a^2*X  1 a^2*X+a a^2 a^2*X+1 a^2*X+1  a a^2*X+a  1 a^2 a^2*X+a^2  1  a  1 a*X a^2*X+1 a*X+a^2 X+a^2  1  1  X a^2*X a*X+a a^2 X+1  1 a*X+a a*X  1  1 a^2*X a^2*X+1  1 a*X+a^2
 0  0  1  1  a a^2  1 X+1  1  a  0  X a^2 a^2 a*X+a^2 a*X+a X+1 X+a  a  1 a^2*X+a^2 a*X+a a*X+1  1  X a^2*X+a a*X+a^2 a*X+a^2  0  X a^2*X+1  1 a*X X+a^2  0 X+a a*X X+a^2 a^2*X+a^2
 0  0  0 a^2*X  0  0  0  X  X  X a^2*X a*X a^2*X a^2*X a*X a*X a*X a*X  X a^2*X  X  0 a^2*X a*X a*X  X  0 a^2*X a^2*X  0 a^2*X  0 a^2*X  0  0 a^2*X a*X a^2*X  0
 0  0  0  0  X a^2*X a*X  X a^2*X a*X a*X  X  X a*X a*X  0  X a*X  0  X a^2*X a^2*X a^2*X a*X  0  X a*X a^2*X  X a*X  0 a^2*X  X  0  X  0 a^2*X a^2*X a^2*X

generates a code of length 39 over F4[X]/(X^2) who´s minimum homogenous weight is 103.

Homogenous weight enumerator: w(x)=1x^0+504x^103+453x^104+360x^105+384x^106+2592x^107+747x^108+1176x^109+744x^110+5532x^111+1854x^112+2304x^113+1200x^114+8352x^115+2562x^116+3936x^117+1920x^118+10800x^119+2745x^120+3288x^121+1488x^122+7392x^123+1338x^124+1224x^125+408x^126+1692x^127+408x^128+42x^132+66x^136+15x^140+9x^144

The gray image is a linear code over GF(4) with n=156, k=8 and d=103.
This code was found by Heurico 1.16 in 90.6 seconds.